(Solution) - Consider a study to investigate a certain suspected disease causing agent -(2025 Original AI-Free Solution)

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Consider a study to investigate a certain suspected disease-causing agent. One thousand people are to be chosen at random from the population; each individual is to be classified as diseased or not diseased and as exposed or not exposed to the agent. The results are to be cast in the following contingency table:

Let EY and EN denote exposure and nonexposure and let DY and DN denote presence and absence of the disease. Express each of the following statements in terms of conditional probabilities.
(a) The disease is more common among exposed than among nonexposed people.
(b) Exposure is more common among diseased people than among nondiseased people.
(c) Exposure is more common among diseased people than is nonexposure.
(d) A majority of diseased people are exposed.
(e) A majority of exposed people are diseased.
(f) Exposed people are more likely to be diseased than are nonexposed people.
(g) Exposed people are more likely to be diseased than to be nondiseased.